On linearisation and existence of preduals
| Autor: | Kruse, Karsten |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Rendiconti del Circolo Matematico di Palermo Series 2 73 (2024), 1591-1615 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s12215-024-01004-8 |
| Popis: | We study the problem of existence of preduals of locally convex Hausdorff spaces. We derive necessary and sufficient conditions for the existence of a predual with certain properties of a bornological locally convex Hausdorff space $X$. Then we turn to the case that $X=\mathcal{F}(\Omega)$ is a space of scalar-valued functions on a non-empty set $\Omega$ and characterise those among them which admit a special predual, namely a strong linearisation, i.e. there are a locally convex Hausdorff space $Y$, a map $\delta\colon\Omega\to Y$ and a topological isomorphism $T\colon\mathcal{F}(\Omega)\to Y_{b}'$ such that $T(f)\circ \delta= f$ for all $f\in\mathcal{F}(\Omega)$. Comment: The former version arXiv:2307.09167v1 of this paper is split into two parts. This is the first part. arXiv admin note: text overlap with arXiv:2307.09167 |
| Databáze: | arXiv |
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